Remark 5.1.9 
As noted prior to its statement,
theorem:counterexample contradicts
[1]},
[2]}, and
[3]}, which claim, for example, that any irreducible flat vector bundle on a smooth proper curve of genus at least 2 admits a semistable isomonodromic deformation. We now explain the gaps in the proofs of
those results. The error in [1]} occurs in
[1]}; the issue is that the map denoted
\(f^*\nabla \)  in diagram (4.14) does not in general exist. The proof works
correctly if \(G=\operatorname{GL}_2\) . An identical error occurs in [2]}. A different argument is given in [3]}.
There, the error occurs in the proof of [3]},
in which the large diagram claimed to be commutative does not in general commute.

